Redesigning the SSS (warning! lots of math)

While it is nice to short stack on a table with a lot of dumb big stacks that can't adapt to your play, that just isn't possible anymore. Playing such a supertight starting hand range just isn't possible anymore. I had fun with a graphing calculator figuring out what you should raise if your opponents play optimally against you. I made the following assumptions:

-You will raise x% of your hands to 3bb
-Each opponent reraises 0.5x% when you raise
-If you get reraised then you go broke with 0.5x% or exactly half of what you raised with. This will result in every all in you play being neutral EV since both handranges are exactly the same.

Using these assumptions I came up with the following formula to calculate the exact % of the time I should be raising from each position. Here it is. Skip a bit if you are not a math nerd like me.

y = x(1.5(1 - 0.5x)^p - 3/2(1 - (1 - 0.5x)^p))

This formula will calculate your average profit per hand where x is the amount of the time that you raise and p is the number of players left to act after you. To explain this dog's breakfast formula:

(1 - 0.5x)^p represents how often every player will fold to you and you take down the blinds. This is multiplied by 1.5 which is the amount that you win by taking down the blinds.

1 - (1 - 0.5x)^p thus represents how often you will be reraised. In this scenario you will either go broke (which is breakeven) or you will fold (and lose 3bb). Half the time you go broke and break even which is why it is 3/2.

1.5(1 - 0.5x)^p - 3/2(1 - (1 - 0.5x)^p therefore represents the EV calculation per hand assuming you raise x%. However this formula does not take into account how often you fold. You could just play AA KK QQ and the average profit per hand based on this formula would be huge but the total number of hands you play would be nothing. All this must be multiplied again by x to come up with the final formula.

And here are the approximate numbers for each position to raise assuming a 9 handed table.

This formula probably does not make sense for sb. In the sb you play out of position with a wide range that contains many hard-to-play hands. I would recommend just playing push-or-fold to save the headache since you don't lose much by doing it. It is maximum profit to shove about 45% of hands. If you don't play push-or-fold then you actually have to play less than 45% of hands since you will be out of position. I will be shoving or folding every hand I play from the sb unless there is opportunity to exploit the player in the BB.

These are just numbers though. The harder part is WHICH hands do I raise? Which hand is better 77 or AT suited. How do I even go about deciding which hands to play?

Help keep the SSS alive; if for nothing more than to learn something new about poker.

This post has been edited 1 time(s), it was last edited by Grailer: 06.05.2010 22:46.

omg you are a genius , ive been doing a similar thing but i was using standard deviation based on information gathered from poker tracker and using vpip% from each player to calcuate a similar percentage for a raising formulae.

I guess thats why it appears im a maniac because sometimes I get called and get lucky flop when i was really just trying to steal blinds based on standard deviations .

Nice one , but I guess the cats out of the bag now . Although Im guessing you also have a degree in statistics as well right ?

Originally posted by noclaninator
-Each opponent reraises 0.5x% when you raise
-If you get reraised then you go broke with 0.5x% or exactly half of what you raised with. This will result in every all in you play being neutral EV since both handranges are exactly the same.

I disagree with this.

Your PFR is 20% @CO so BTN/SB/BB will 3bet you 10% of the time?
Say you isolate 30% , will they be 3betting 15% of the time? Mixing in some 16-24tableaments where they dont even care about dynamics and stuff.

The 2nd sentence is a bit marginal since you dont equilate your range/hand versus a range. It's easier but definitly you miss the small margins and adding that up within 1 million hands played

If you open raise 20% then it is optimal (or at least close to optimal) for a villain to 3bet 10%. If someone deviates from this, it is your job as a poker player to figure out how they are deviating and adjust accordingly. If I raise button 27% and some guy decides hes going to bluff shove alot then I should be calling my entire range. I made the assumption that other players will play optimally (or at least close to it) but of course they won't.

For example suppose you are UTG with AJ. This is a fold but if there is some kind of tardfish with a vpip of 95% then AJ becomes a profitable raise from UTG. Likewise if you are on the BU and SB and BB both have fold to steal values of over 90% then you are making a mistake if you are not raising 100%.

Raise 50-80% of buttons = WHAAAAAAT? Do you know how often you are going to get shoved (or at least SHOULD get shoved) if you raise this often? I mean if they don't shove 40% against your button raise then great but if they aren't shoving alot against such a loose raise then threads such as this one become useless since I am already crushing everything I play if they don't notice obvious things such as this.

Having read what Gerv said about equilating hands against ranges this is absolutely correct. One assumption I made that is super incorrect is the assumption that you should call off your stack with 50% of your raising range. This is way too loose for sure. Another assumption that I made is opponents should reraise 50% of your range though this isn't off by much.

If you raise AQ+, TT+ (4.68%) from early position then it is correct for them to reraise AK+, QQ+ (2.57%) AK is a slight equity underdog against this range but an EV calculation shows it is a profitable semi bluff. Jacks are also a slight equity dog but not a profitable semi bluff. (On a side note you will lose about 1.5 bb every time you shove Jacks against a UTG raise which is a lot worse than I thought.) This means against UTG you should reraise more than half of his range. If you make the assumptions that I did then you reraise 2.3% which is not enough here.

If you have QQ then you have 40.2% equity and should not call against this range since you need 42.5% equity to call (not counting dead money and rake). AK suited comes even closer at 41.9%. At higher limits like $5/$10 (where the blind dead money quite exceeds the rake) this is a call but on the limits most people play on it is still a fold. My math says you should go broke with 2.3% when it is actually only profitable to go broke with about 1% (though you can call off about 1.66% without losing much). However if you raise AQ+, TT+ from early and only go broke with KK+ then you of course open yourself up to bluff raises not that many people would try it after a UTG raise. Thankfully, people will invariably reraise a UTG raiser with JJ which makes going broke with AKs and QQ profitable. Still, with the assumptions I made we are calling our stack off a bit too light.

What about button? If button raises 28% then by my calculations sb or bb should reraise 14%. This is approximately 55+, A8s+, KTs+, QJs, A9o+, KJo+. Against this range we can call our stack off with 55+, A9s+, KQs, ATo+ which is about 10%. This is less than half of the range. Again with my assumptions we are calling off too light.

So how often should we call off our stack against a reraise? With the UTG we should raise 4.68% and call off 1.66% (so we go broke about 35% of the time). From BU we go broke 10%/28% which AGAIN is about 35%. This suggests to me that we should go broke with 35% of our raising range from any position and NOT 50%.

I guess this means it is time to redo all the calculations. I think raising ranges from all positions will become a tad bit looser. Remember though that these calculations assume optimal play from all villains. When I say you shouldn't go broke with Jacks; I am talking about against the "perfect" opponent and not your typical fish.

Originally posted by Andresart
If you play high-er stakes, you ´ll see that many players OR like 50-90% in btn, and 80-100% in SB. Try to figure out what should be his restealing range bvb to make you opening less hands.

obv u have never played higher stakes than nl25 i guess. opening more than 40% from SB against good players is burning money intentionally

On higher stakes (and I've SSS'd up to $5/$10 before) it may be profitable to raise 50% but it is not as profitable if they adapt PROPERLY (important)

Say you raise 50% from the button. I will adapt by pushing all in with 25%. Other player should adapt the same way. Assuming this I will calculate the EV of playing the button this way as opposed to play

(0.75)(0.75) = 56.25% chance of winning the blinds preflop. 43.75% of the time your raises will be shoved on. Against a 25% range you can call about 25% or half the time that you raise

You win about 0.09bb each time you play the button. This number may not mean a whole lot to you but let me assure you that bigger is better. Let's look at my number 28%

SB and BB will have to reraise 14% if I raise 28%. Against this range I can call 12% profitably. I will win the blinds 73.96% of the time that I raise. 14.88% of the time I will get reraised and have to fold; and 11.16% of the time we will play an all in pot. When the all in pot is played I will average 52% equity for an average win of 0.8bb.

And let me assure you if you raise more than 50% that number WILL go down if your opponents adapt properly. The number that I came up with assumes that your opponents are adapting. If there are two fish in the blinds who fold everything then feel free to raise 100% until they play back at you but the 28% number that I calculated is close to optimal if your opponents are adapting.

Remember YOU CANT USE POSITION POSTFLOP in SSS. When TwiceT says in his videos you should open raise 100% of buttons he is very correct because in BSS you can call any reraise and play position postflop. In SSS you can't play position = tighten up your preflop raising ranges.

I recalculated the "optimal" open raising ranges from each position. The numbers did not become a tad bit looser but a tad tighter for each position. The difference is actually so small that it is negligible.

If any if you still disagree with my 27.6% button raising range then please come to any game I am in and sit to my right. I have not been getting my fair share of seafood yet due to extreme overfishing on pokerstars.